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2002/2003 The $\mathcal{I}$-almost constant convergence of sequences of real functions.
Tomasz Natkaniec
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Real Anal. Exchange 28(2): 481-492 (2002/2003).


Let \(T\) be an infinite set and \(\mathcal{I}\) be a fixed ideal on \(T\). We introduce and study the notion of almost constant convergence of sequences \(\{ f_t\colon t\in T\}\) of real functions with respect to the ideal \(\mathcal{I}\). This notion generalizes discrete convergence, transfinite convergence, and \(\omega_2\)-convergence. In particular, we consider the question when a given family of functions (e.g., continuous, Baire class 1, Borel measurable, Lebesgue measurable, or functions with the Baire property) is closed with respect to this kind of convergence.


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Tomasz Natkaniec. "The $\mathcal{I}$-almost constant convergence of sequences of real functions.." Real Anal. Exchange 28 (2) 481 - 492, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

MathSciNet: MR2010331

Primary: 26A03
Secondary: 03E35 , 26A15 , 28A05

Keywords: $\mathcal{I}$-almost constant family , $\mathcal{I}$-convergence , 0-1 set , Additivity , covering , ideal of sets , point-$\mathcal{I}$-disjoint family

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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